A great many number of illumination applications use optical lightguides to deliver luminous radiation from a source to a specific target or region of space. For examples, light guides are used in backlight display systems, general illumination (e.g., luminaries), and medical devices, such as endoscopes. For example, see U.S. Pat. Nos. 6,775,460, 5,949,933, 6,474,827, 6,002,829, 6,948,832, 5,136,480, 5,613,751, and 6,910,783. The lightguides or light directing optical elements describe in these patents rely on either triangular or trapezoidal shaped surfaces, microprism or microlense arrays, undulating ribbon-like structures, prismatic surface indentations, or rounded notches, to extract light. Although useful with their respective light sources in their particular applications, these light directing optical elements do not efficiently use total internal reflection to deliver light such as realized from structures of the present invention.